Carry a small notebook (paper or electronic) at all times, and write down new
words when you come across them. Test yourself on new words you learn; try to
use these new words, and look for them in things you read.
Vocabulary textbooks can be a useful way of studying words in a structured way,
with words being groups by subject.
Some possible methods of increasing your vocabulary are suggested below.

The British National Corpus (BNC) is a 100 million word collection of
samples of written and spoken language from a wide range of sources, designed
to represent a wide cross-section of current British English, both spoken and
written.
You can see some example sentences showing how a word or phrase is used by searching
the British National Corpus; see http://sara.natcorp.ox.ac.uk/lookup.html

Word frequencies

One way for advanced English students to increase their vocabulary is to learn
words according to the order of frequency of usage. The dictionary "Collins
Cobuild English Dictionary for Advanced Learners" contains information
on the frequency of usage of the words it lists, helping the user to concentrate
on the most common words first. For details, see: Dictionary.
A list of the most common words in British English is contained in the file
lemma.num available free from the site: http://www.itri.bton.ac.uk/~Adam.Kilgarriff.

When you learn a new word, why not see if there are other words with similar
or opposite meanings (synonyms or antonyms) and study these at the same time?
One way of doing this would be to use Roget's Thesaurus, which is available
online at: http://www.thesaurus.com/roget.
Solving crossword puzzles (the ones with simple or "straight" clues
are easier) can be a good way to increasing vocabulary. You can use a thesaurus
or a crossword dictionary to help you. Crosswords appear every day in most British
newspapers, or books of crossword puzzles can be bought.
Some electronic dictionaries provide links to similar or opposite words, helping
you to expand your vocabulary

Learning about the origin of a word or phrase (its etymology) can make
the study of vocabulary more interesting, and can also help you to understand
the connections between words. There is an online dictionary of etymology at:
http://www.etymonline.com.

Many English words originated from Latin and Greek. Advanced students
may find it helpful to study at the same time words which come from the same word
stem. Did you know that the word "telephone" comes from the Greek roots
"tele" (meaning far) and "phone" (meaning sound)? "Tele"
is the link between telephone (far hearing), television (far sight), telegraph
(far writing), telepathy (far feeling). "Phone" is the link between
telephone (far hearing) phonetic (connected with hearing), microphone (small hearing).
A list of Latin and Greek roots and examples of words which use them is available
from the Buncha Roots site at http://abasiccurriculum.com/homeschool/roots